Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology

Acharjee, Santanu; Papadopoulos, Kyriakos; Tripathy, Binod Chandra

doi:10.5269/bspm.v38i1.34701

Cited by 5 publications

(5 citation statements)

References 23 publications

(28 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Definition 2.1. [1] Let X be a non-emptyset. A collection P ⊆ 2 X is called a primal on X if it satisfies the following conditions: A topological space (X, τ ) with a primal P on X is called a primal topological space and denoted by (X, τ, P).…”

Section: Preliminariesmentioning

confidence: 99%

“…It was introduced by Choquet [15] in 1947 and studied by many authors in [6,7,8,9,10,11,12,13,14]. Recently, Acharjee et al introduced a new classical structure called primal [1]. They define the notion of primal topological space by utilizing two new operators and investigate many fundamental properties of this new structure and these two operators.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

ÖZKOÇ,

KÖSTEL

2024

Preprint

View full text Add to dashboard Cite

The main purpose of this paper is to introduce and study two new operators $(\cdot)_{R}^{\diamond}$ and $cl_{R}^{\diamond}(\cdot)$ via primal which is a new notion. We also show that the operator $cl_{R}^{\diamond}(\cdot)$ is a Kuratowski closure operator, while the operator $(\cdot)_{R}^{\diamond}$ is not. In addition, we prove that the topology on $X$, shown as $\tau_{R}^{\diamond}$, obtained by means of the operator $cl_{R}^{\diamond}(\cdot)$ is finer than $\tau_{\delta}$, where $\tau_{\delta}$ is the family of $\delta$-open subsets of a space $(X,\tau)$. Moreover, we not only obtain a base for the topology $\tau_{R}^{\diamond}$ but also prove many fundamental results concerning this new structure. Furthermore, we give many counterexamples related to our results. 2020 AMS Classifications: 54A05; 54B99; 54C60.

show abstract

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

ÖZKOÇ,

KÖSTEL

2024

Preprint

View full text Add to dashboard Cite

show abstract

“…During the preparation of this paper with refer to Kilicman and Salleh [6], some open questions were raised. Some answers of these questions are affirmative and one counter example is proved by Acharjee et al in [44]; using interlocking and nest in a bitopological space. Notions of interlocking and nest can be found in [ 45].…”

Section: Sufficiencymentioning

confidence: 99%

$p$-$\mathcal{I}$-generator and $p_1$-$\mathcal{i}$-generator in bitopology

Acharjee

Tripathy

2018

bspm

Self Cite

View full text Add to dashboard Cite

In this article we have investigated the relations of $p$-$\mathcal{I}$-generator, $p_1$-$\mathcal{I}$-generator with $p$-Lindel\"{o}f and $p_1$-Lindel\"{o}f using $\tau_i$-codense, $(i,j)$-meager, $(i,j)$-nowhere dense and perfect mapping of bitopological space. The relations between $p$-compactness, $p$-Lindel\"{o}fness, $p_1$-Lindel\"{o}fness and topological ideal, $(i,j)$-meager, $(i,j)$-Baire space in bitopological space are investigated. Some properties are studied on product bitopology using perfect mapping. It can be found that bitopological space has many applications in real life problems. Hence, we hope that this theory will help to fulfill some interlinks which may have applications in near future.

show abstract

“…Pervin [20] extended the concept of continuity and connectedness in a bitopological space. For recent theoretical works in bitopological space, one may refer to Acharjee and Tripathy [5], Acharjee et al [3], Acharjee et al [4] and many others. Recently, bitopological space has been applied in many areas of science and social science.…”

Section: Introductionmentioning

confidence: 99%

Transitive maps in bitopological dynamical systems

Acharjee

Goswami²,

Kumar

2021

Filomat

Self Cite

View full text Add to dashboard Cite

This paper introduces fundamental ideas of bitopological dynamical systems. Here, notions of bitopological transitivity, point transitivity, pairwise iterated compactness, weakly bitopological transitivity, etc. are introduced. Later, it is shown that under pairwise homeomorphism, weakly point transitivity implies weakly bitopological transitivity. Moreover, under pairwise homeomorphism; pairwise compactness and pairwise iterated compactness are found to be equivalent. Later, we apply our results in the development process of a human embryo from the zygote until birth. During the process of biological application, we disprove conjecture 1 of Nada and Zohny [S. I. Nada, H. Zohny, An application of relative topology in biology. Chaos, Solitons and Fractals, 42 (2009) 202-204].

show abstract

Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology

Cited by 5 publications

References 23 publications

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

$p$-$\mathcal{I}$-generator and $p_1$-$\mathcal{i}$-generator in bitopology

Transitive maps in bitopological dynamical systems

Contact Info

Product

Resources

About